Interest Rate Curve

Port Finance uses Aave's interest rate model where the rate is determined by the utilization of the protocol. It employs a two segment interest rate model, where the second slope is steeper than the first to incentivize more depositing when utilization ratio is high.
Mathematically, we use the following interest rate model:
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U<Uoptimal:Rcurr=R0+UtUoptimalRslope1U < U_{optimal}: R_{curr} = R_{0}  + \frac{U_{t}}{U_{optimal}} R_{slope1}
U<Uoptimal​:Rcurr​=R0​+Uoptimal​Ut​​Rslope1​
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U≥Uoptimal:Rt=R0+Rslope1+Ut−Uoptimal1−UoptimalRslope2U \geq U_{optimal}: R_{t} = R_{0} + R_{slope1} + \frac{U_{t} - U_{optimal}}{1 - U_{optimal}} R_{slope2}U≥Uoptimal​:Rt​=R0​+Rslope1​+1−Uoptimal​Ut​−Uoptimal​​Rslope2​
When U < U Optimal, the rate increases slowly with utilization.
When U >= U Optimal the borrow interest rate increases sharply to incentivizes more deposit and avoid liquidity risk.

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